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Simplifying (2x2 + -28x + 49) + -20 = 0 Reorder the terms: (49 + -28x + 2x2) + -20 = 0 Remove parenthesis around (49 + -28x + 2x2) 49 + -28x + 2x2 + -20 = 0 Reorder the terms: 49 + -20 + -28x + 2x2 = 0 Combine like terms: 49 + -20 = 29 29 + -28x + 2x2 = 0 Solving 29 + -28x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 14.5 + -14x + x2 = 0 Move the constant term to the right: Add '-14.5' to each side of the equation. 14.5 + -14x + -14.5 + x2 = 0 + -14.5 Reorder the terms: 14.5 + -14.5 + -14x + x2 = 0 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + -14x + x2 = 0 + -14.5 -14x + x2 = 0 + -14.5 Combine like terms: 0 + -14.5 = -14.5 -14x + x2 = -14.5 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = -14.5 + 49 Reorder the terms: 49 + -14x + x2 = -14.5 + 49 Combine like terms: -14.5 + 49 = 34.5 49 + -14x + x2 = 34.5 Factor a perfect square on the left side: (x + -7)(x + -7) = 34.5 Calculate the square root of the right side: 5.873670062 Break this problem into two subproblems by setting (x + -7) equal to 5.873670062 and -5.873670062.Subproblem 1
x + -7 = 5.873670062 Simplifying x + -7 = 5.873670062 Reorder the terms: -7 + x = 5.873670062 Solving -7 + x = 5.873670062 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 5.873670062 + 7 Combine like terms: -7 + 7 = 0 0 + x = 5.873670062 + 7 x = 5.873670062 + 7 Combine like terms: 5.873670062 + 7 = 12.873670062 x = 12.873670062 Simplifying x = 12.873670062Subproblem 2
x + -7 = -5.873670062 Simplifying x + -7 = -5.873670062 Reorder the terms: -7 + x = -5.873670062 Solving -7 + x = -5.873670062 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -5.873670062 + 7 Combine like terms: -7 + 7 = 0 0 + x = -5.873670062 + 7 x = -5.873670062 + 7 Combine like terms: -5.873670062 + 7 = 1.126329938 x = 1.126329938 Simplifying x = 1.126329938Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.873670062, 1.126329938}
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